Useful martingales for stochastic storage processes with L\'evy-type input
Abstract
In this paper we generalize the martingale of Kella and Whitt to the setting of L\'evy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge to zero a.s. and in L2. The reflected L\'evy-type process is considered as an example.
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